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The problem you shared is about calculating the time it takes to fill a cylindrical tank with liquid waste. Here's the solution breakdown:

### Given:
- **Height of the cylinder (h):** 30 cm
- **Diameter of the cylinder:** 14 cm (so the radius \( r = \frac{14}{2} = 7 \) cm)
- **Flow rate:** 10 mL per minute
- We need to find the total time required to fill the tank.

### Step 1: Calculate the Volume of the Cylinder
The formula for the volume \( V \) of a cylinder is:
\[
V = \pi r^2 h
\]
Substitute the values of \( r = 7 \) cm and \( h = 30 \) cm into the formula:
\[
V = \pi \times 7^2 \times 30 = \pi \times 49 \times 30 = 1470 \pi \, \text{cm}^3
\]
Approximating \( \pi \approx 3.1416 \):
\[
V \approx 1470 \times 3.1416 \approx 4618.44 \, \text{cm}^3
\]

### Step 2: Convert Volume to mL
Since 1 cm³ = 1 mL, the volume of the cylinder is approximately 4618.44 mL.

### Step 3: Calculate the Time to Fill the Cylinder
Since the liquid flows at 10 mL per minute, the time required to fill the entire tank is:
\[
\text{Time} = \frac{\text{Volume}}{\text{Flow rate}} = \frac{4618.44 \, \text{mL}}{10 \, \text{mL/min}} = 461.84 \, \text{minutes}
\]

### Step 4: Round to the Nearest Option
The closest answer to 461.84 minutes is **462 minutes**, which corresponds to option **C**.

### Final Answer:
The time required to fill the cylinder is **462 minutes** (Option C).

---

Would you like more details on any step or further explanations? Here are 5 related questions to expand the topic:

1. How would the solution change if the radius of the cylinder doubled?
2. What if the flow rate was halved, how long would it take to fill the cylinder?
3. How do we derive the formula for the volume of a cylinder?
4. What units would be used if the measurements were in meters instead of centimeters?
5. How can we calculate the time for irregularly shaped containers?

**Tip:** Always double-check units to ensure the correct conversions are used in volume and flow calculations.

Sebuah alat tampung limbah cairan berbentuk tabung, dengan ukuran tinggi 30cm dan diameter 14cm. Jika cairan limbah yang masuk kedalam tabung memiliki waktu konstan 10 ml tiap menit, waktu yang dibutuhkan sampai tabung bisa terisi penuh adalah.... menit.

Calculate the time required to fill a cylindrical tank of height 30 cm and diameter 14 cm with a constant flow rate of 10 mL per minute. Learn how to apply volume formulas and unit conversions. Suitable for students in Grades 9-11.

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